A fast finite difference method for three-dimensional time-dependent space-fractional diffusion equations and its efficient implementation

By Hong Wang, Ning Du. 2013

64 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Numerical Analysis

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Modeling and Simulation

1. Fawang Liu
2. Changpin Li
3. Ian L Turner
4. Vo Anh
5. Fanhai Zeng
6. G. Em Karniadakis
7. Lu Lu
8. Kevin Burrage

In Numerical Analysis

1. Changpin Li
2. Fawang Liu
3. Ian L Turner
4. Vo Anh
5. Fanhai Zeng
6. Kevin Burrage
7. G. Em Karniadakis
8. Guofei Pang

Citations in the corpus

• fPINNs: Fractional Physics-Informed Neural Networks (2018, methodology): “In [36, 37, 38, 39], only the 3D extension of the Riesz space-fractional derivatives is considered, which differs from the directional fractional Laplacian of our interest; in [40], Riesz fractional Laplacian is first regularized by singularity subtraction and then approximated by using trapezoidal ”
• A Petrov–Galerkin finite element method for variable-coefficient fractional diffusion equations (2015, methodology): “A careful study needs to be carried out to investigate whether the stiffness matrix has certain Toeplitz-like structure as in the case of finite difference methods, so that a fast Fourier transform based fast Krylov subspace iterative method can be developed which has an almost linear computational ”
• A Crank-Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation (2014, methodology): “Some fast solution techniques were developed in [43, 44, 45, 40, 41] to solve the space fractional differential equations, in which the fractional derivative operators are discretized by the finite difference methods that yield a coefficient matrix with special structures.”
• A Fast Finite Difference Method for Three-Dimensional Time-Dependent Space-Fractional Diffusion Equations with Fractional Derivative Boundary Conditions (2017, background): “These observations are consistent with those in the context of Dirichlet boundary-value problem of time-dependent of space-fractional diffusion equations [27].”
• Adaptive finite element method for fractional differential equations using hierarchical matrices (2016, background): “This results in efficient matrix-vector multiplications [20, 27, 41, 38, 16], which in conjunction with effective preconditioners lead to enhanced efficiency [19, 39, 15, 22, 25].”
• Time two-mesh algorithm combined with finite element method for time fractional water wave model (2018, unknown): “In view of the difficulty for solving the analytic solutions, increasing scholars have started to study some effective numerical methods for solving complex FPDEs with time, space and space-time fractional derivatives, which include finite difference methods [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1”